Prime factorization of $$$4370$$$

Find the prime factorization of $$$4370$$$.

Start with the number $$$2$$$.

Determine whether $$$4370$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4370$$$ by $$${\color{green}2}$$$: $$$\frac{4370}{2} = {\color{red}2185}$$$.

Determine whether $$$2185$$$ is divisible by $$$2$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$3$$$.

Determine whether $$$2185$$$ is divisible by $$$3$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$5$$$.

Determine whether $$$2185$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$2185$$$ by $$${\color{green}5}$$$: $$$\frac{2185}{5} = {\color{red}437}$$$.

Determine whether $$$437$$$ is divisible by $$$5$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$7$$$.

Determine whether $$$437$$$ is divisible by $$$7$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$11$$$.

Determine whether $$$437$$$ is divisible by $$$11$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$13$$$.

Determine whether $$$437$$$ is divisible by $$$13$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$17$$$.

Determine whether $$$437$$$ is divisible by $$$17$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$19$$$.

Determine whether $$$437$$$ is divisible by $$$19$$$.

It is divisible, thus, divide $$$437$$$ by $$${\color{green}19}$$$: $$$\frac{437}{19} = {\color{red}23}$$$.

The prime number $$${\color{green}23}$$$ has no other factors then $$$1$$$ and $$${\color{green}23}$$$: $$$\frac{23}{23} = {\color{red}1}$$$.

Since we have obtained $$$1$$$, we are done.

Now, just count the number of occurences of the divisors (green numbers), and write down the prime factorization: $$$4370 = 2 \cdot 5 \cdot 19 \cdot 23$$$.

The prime factorization is $$$4370 = 2 \cdot 5 \cdot 19 \cdot 23$$$A.